> It does seem that the richer the mathematics teachers' knowledge within and> about the mathematical arts ... and within and about the psychology of> mathematical comprehension ... the better they are at making curricular> mathematics common-sensible to students. For sure, there are countries> whose teachers ... in the norm ... are better educated in both of those> areas.>

Lets consider an analogy. I just came back from an intensivelymathematical conference in that professionals from many walks of lifeconverged to discuss symbolic manipulation and modeling. We hadastronomer types (NASA), publishers, linguists, cartographers (ESRI),and quite a few robotics folks. We flew in from all over the world,which accounts for the nickname of "flying circus" although there's aMonty Python angle as well.

Some of the smartest people there, like Tatia, had pretty thickaccents when speaking English. She's from Brazil. Lots of Britishaccents as well. Our chairman (foundation) was from Manchester.

This is a picture of a well educated, mathematically well endowedcross-section of the world's population. We met in Santa Clara,Silicon Valley.

> So, it would seem that American teachers might already be about as good as> could be expected ... in doing what they are trying to do (implementing> parrot-training curricula) ... with "undisciplined" American students who> know only how to try to do what (parroting) they are trying to do. The> tragedy is that (try as they must) the students presently cannot learn> curricular mathematics as mathematical common sense ... because the> curricula that teachers implement are not scientifically designed to be> mathematically common-sensible to students.>> Cordially,>> Clyde>

Why do we care who's "American" again? What foul brainwashing made itimportant where you happened to pop out on the surface of a sphere?What silly / arbitrary partitioning was applied to make these peoplehate each other and justify their petty wars? Ah yes, nations,statism. Hardly mathematically beautiful. Come to think of it, it'shard to find mathematically mature people who think the nation stateminded have much serious to offer. When it comes to management, it's"think globally, act locally". If you don't know how to do that, thenyou can be a puppet in front of a teleprompter telling people whatthey want to hear -- but a mathematician you won't be, most probably.